Thousands of protesters are expected to join the parents of Trayvon Martin at a rally in Florida amid growing anger and increasing pressure on authorities to arrest the black teenager's killer.

Police in Sanford said that up to 10,000 people could take part in the demonstration, which comes exactly a month after the 17-year-old was shot dead by self-appointed neighbourhood watch volunteer George Zimmerman.

The rally is one of a series of events taking place across the US on Monday to protest against the handling of the case and the perceived failure to hold the 28-year-old to account over Martin's death.

Over the weekend, vigils were held in churches across America in memory of Martin, who was killed as he walked back to the home of his father's girlfriend after a trip to nearby convenience store.

A number of preachers wore hooded tops in a sign of solidarity with the dead teenager's supporters. Martin was wearing a hoodie at the time of the killing.

At the Macedonia Missionary Baptist Church in Eatonville, Florida, the Rev Jesse Jackson told a packed congregation on Sunday that "the blood of the innocent has power".

Jackson likened Martin to Emmett Till, the 14-year-old who was mutilated and murdered in 1955 for allegedly whistling at a white woman.

He also listed Martin alongside assassinated civil rights leaders Medgar Evers and Martin Luther King Jr, adding that his "martyr" death should be used to draw attention to long-standing issues affecting the black community.

Rev Jackson is expected to attend Monday's rally and a subsequent town hall meeting in Sanford.

He will be joined at the event by the teenager's parents Tracy Martin and Sybrina Fulton, and fellow civil rights leader the Rev Al Sharpton.

Sanford authorities are expecting a large turnout at the demonstration, and have cordoned off streets around Fort Mellon Park, which has become a focal point of protest since Martin's death.

A spokeswoman for Sanford police said they had been told that between 4,000 and 10,000 demonstrators will take part in the action.

It is the largest of a series of protests and demonstrations planned for Monday across the US, including one planned outside the US justice department in Washington DC.

Martin's parents will also take their concerns over the handling of the investigation to civic leaders at a town hall meeting in Sanford on Monday evening. It is the first such meeting since Martin's death thrust Sanford into the news.

Rev Sharpton is likely to attend the discussions. On Sunday, he held talks with Martin's parents and their legal representatives over the case.

Sharpton tweeted this morning: "Spent much of last night meeting with the parents and lawyers of Trayvon Martin about the legal and movement strategy for justice."

Photograph: AP

Anger has grown in the weeks following Martin's death, amid claims of police failings in the case and an alleged racial element to the killing.

Last week, Sanford police chief Bill Lee stepped down temporarily. He was joined soon after by state attorney Norman Wolfinger, who recused himself following criticism.

But neither development, nor the intervention of President Barack Obama, who delivered a personal statement calling for a thorough investigation into Martin's deth, have quietened the discontent.

George Zimmerman claims he killed in self-defence and that the teenager was acting suspiciously at the time of the incident, with a hooded top pulled over his head.

Supporters of Zimmerman have cited Florida's controversial "stand your ground" legislation, which authorises the use of lethal force in certain situations.

But it has been alleged that Zimmerman may have profiled Martin due to his race. And a recorded conversation between Zimmerman and a 911 operator shortly before the incident may contain a racial slur – although this has been disputed.

Zimmerman's lawyer, Craig Sooner, has denied that his client acted out of prejudice.

Nonetheless, the allegations have added to the anger felt and have led to widespread protest among the black community.

Over the weekend, the New Black Panther Party – a fringe organisation accused by the US government of fostering an anti-white hate agenda –put a $10,000 bounty on Mr Zimmerman's head.

Announcing the reward, the group's leader, Mikhail Muhammad, demanded an "eye for an eye" in relation to the Martin death.